Robust H∞ filtering for a class of Markovian jump systems with time‐varying delays based on delta operator approach

In this paper, the robust H_∞ filtering problem for a class of discrete Markovian jump systems with time‐varying delays and linear fractional uncertainties is investigated based on delta operator approach. Based on Lyapunov‐Krasovskii functional in delta domain, new delay‐dependent sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired jump H_∞ filter is given. The proposed method can unify some previous related continuous and discrete systems into the delta operator systems framework. Numerical examples are given to illustrate the effectiveness of the developed techniques. © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust stability and H∞ control for uncertain discrete Markovian jump singular systems with mode‐dependent time‐delay

The robust stochastic stability, stabilization and H_∞ control for mode‐dependent time‐delay discrete Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a standard linear system, and delay‐dependent linear matrix inequalities (LMIs) conditions for the mode‐dependent time‐delay discrete Markovian jump singular systems to be regular, causal and stochastically stable, and stochastically stable with γ‐disturbance attenuation are obtained, respectively. With these conditions, robust stabilization problem and robust H_∞ control problem are solved, and the LMIs sufficient conditions are obtained. A numerical example illustrates the effectiveness of the method given in the paper. Copyright © 2008 John Wiley & Sons, Ltd.     

Delay‐dependent stability criterion and H∞ analysis for Markovian jump systems with time‐varying delays

This paper deals with the problems of stochastic stability and H_∞ analysis for Markovian jump linear systems with time‐varying delays. In terms of linear matrix inequalities, a less conservative delay‐dependent stability criterion for Markovian jump systems is proposed by constructing a different Lyapunov‐Krasovskii functional and introducing improved integral‐equalities approach, and a sufficient condition is derived from the H_∞ performance. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

H∞ filtering for singular Markovian jump systems with time delay

The problem of H_∞ filtering is considered for singular Markovian jump systems with time delay. In terms of linear matrix inequality (LMI) approach, a delay‐dependent bounded real lemma (BRL) is proposed for the considered system to be stochastically admissible while achieving the prescribed H_∞ performance condition. Based on the BRL and under partial knowledge of the jump rates of the Markov process, both delay‐dependent and delay‐independent sufficient conditions that guarantee the existence of the desired filter are presented. The explicit expression of the desired filter gains is also characterized by solving a set of strict LMIs. Some numerical examples are given to demonstrate the effectiveness of the proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.     

Delay‐dependent passivity and passification for uncertain Markovian jump systems with time‐varying delays

This paper deals with the problems of passivity analysis and passivity‐based controller design for Markovian jump systems with both time‐varying delays and norm‐bounded parametric uncertainties. Firstly, new delay‐dependent conditions for the considered system to be passive are obtained by using a mode‐dependent Lyapunov functional and by introducing some slack variables. These conditions are expressed by means of LMIs that are easy to check. It is shown through a numerical example that the obtained passivity conditions are less conservative than the existing ones in the literature. Secondly, the passification problem is investigated. On the basis of the obtained passivity conditions, dynamic output‐feedback controllers are designed, which ensure that the resulting closed‐loop system is passive. The effectiveness of the proposed design method is demonstrated by a numerical example. Copyright © 2011 John Wiley & Sons, Ltd.     

H∞ filtering for singular systems with time‐varying delay

This paper is concerned with the delay‐dependent H_∞ filtering problem for singular systems with time‐varying delay in a range. In terms of linear matrix inequality approach, the delay‐range‐dependent bounded real lemmas are proposed, which guarantee the considered system to be regular, impulse free and exponentially stable while satisfying a prescribed H_∞ performance level. The sufficient conditions are proposed for the existence of linear H_∞ filter. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.     

Delay‐range‐dependent robust H∞ filtering for uncertain systems with interval time‐varying delays

This paper is concerned with the problem of delay‐range‐dependent robust H_∞ filtering for systems with time‐varying delays in a range. The aim of this problem is to design a filter such that, for all admissible uncertainties, the filtering error system is robustly asymptotically stable with a prescribed H_∞ level. The desired filter can be constructed by solving a set of linear matrix inequalities (LMIs). An illustrative numerical example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust finite‐time H∞ synchronization for uncertain discrete‐time systems with nonhomogeneous Markovian jump: Observer‐based case

In this article, the problem of robust finite‐time H_∞ synchronization control is investigated for a class of uncertain discrete‐time master‐slave systems with Markovian switching parameters in the observer‐based case. Parameter uncertainties are assumed to be norm‐bounded, and the polyhedral character is utilized to describe the transition probabilities of nonhomogeneous Markov chain. By using stochastic Lyapunov function method and finite‐time analysis techniques, novel sufficient conditions that include the master‐slave parameters are obtained for designing an observer‐based finite‐time H_∞ synchronization control law in terms of linear matrix inequalities. The effectiveness of the proposed theoretical scheme is finally demonstrated by some simulations.     

Robust H ∞ filtering for singular time‐delayed systems with uncertain Markovian switching probabilities

This paper is concerned with the robust H _∞ filter design for a class of uncertain singular time‐delayed Markovian jump systems, whose transition rate matrix has elementwise bounded uncertainties. By the LMI approach, a novel bounded real lemma is proposed such that the singular Markovian jump system is robustly exponentially mean‐square admissible with a prescribed H _∞ performance index. Based on this, a sufficient condition for the existence of a robust H _∞ filter is developed in terms of LMIs. Finally, a numerical example is provided to show the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Delay‐dependent robust control for singular discrete‐time Markovian jump systems with time‐varying delay

The problem of delay‐dependent robust stabilization for uncertain singular discrete‐time systems with Markovian jumping parameters and time‐varying delay is investigated. In terms of free‐weighting‐matrix approach and linear matrix inequalities, a delay‐dependent condition is presented to ensure a singular discrete‐time system to be regular, causal and stochastically stable based on which the stability analysis and robust stabilization problem are studied. An explicit expression for the desired state‐feedback controller is also given. Some numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Exponential H∞ filtering for switched linear systems with interval time‐varying delay

This paper deals with the problem of exponential H_∞ filtering for a class of continuous‐time switched linear system with interval time‐varying delay. The time delay under consideration includes two cases: one is that the time delay is differentiable and bounded with a constant delay‐derivative bound, whereas the other is that the time delay is continuous and bounded. Switched linear filters are designed to ensure that the filtering error systems under switching signal with average dwell time are exponentially stable with a prescribed H_∞ noise attenuation level. Based on the free‐weighting matrix approach and the average dwell technology, delay‐dependent sufficient conditions for the existence of such a filter are derived and formulated in terms of linear matrix inequalities (LMIs). By solving that corresponding LMIs, the desired filter parameterized matrices and the minimal average dwell time are obtained. Finally, two numerical examples are presented to demonstrate the effectiveness of the developed results. Copyright © 2008 John Wiley & Sons, Ltd.     

Reliable exponential filtering for singular Markovian jump systems with time‐varying delays and sensor failures

This paper deals with the problem of exponential filtering for singular Markovian jump systems with time‐varying delays subject to sensor failures. The main objective is to design a reliable filtering such that the considered filtering error system in the presence of a time‐varying delay and sensor failures is mean‐square exponentially admissible with a specified decay rate and simultaneously satisfies an performance. First, the delay interval is partitioned into m subintervals and a novel mode‐dependent stochastic Lyapunov‐Krasovskii functional is constructed. By using the reciprocally convex inequality in each subinterval, sufficient conditions of exponential performance analysis are developed for the considered filtering error system. Then, based on these conditions, the existence conditions of the desired reliable filter are derived and the filter parameters are obtained. It should be mentioned that all the results presented here are not only dependent on the time delay but also dependent on the decay rate and the partitioning size. Furthermore, all the conditions are established in terms of strict linear matrix inequalities. Finally, two numerical examples are given to illustrate the less conservatism and effectiveness of the proposed methods.     

Delay‐range‐dependent H∞ control for Markovian jump systems with mode‐dependent time delays

This paper considers mean‐square exponential stability and H_∞ control problems for Markovian jump systems (MJSs) with time delays which are time‐varying in an interval and depend on system mode. By exploiting a novel Lyapunov‐Krasovskii functional which takes into account the range of delay, and by making use of some techniques, new delay‐range‐dependent stability result and bounded real lemma for MJSs are obtained, where the introduction of the lower bound of delay is shown to be advantageous for reducing conservatism. Moreover, a sufficient condition for the solvability of the H_∞ control problem is derived in terms of linear matrix inequalities. Finally, illustrative examples are presented to show the advantage and effectiveness of the proposed approaches. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Exponential H ∞ filtering for singular systems with Markovian jump parameters

This paper is concerned with the H _∞ filter design for continuous‐time singular systems with Markovian jump parameters, whose system mode is transmitted through an unreliable network. In contrast to the traditionally mode‐dependent or mode‐independent filtering method, a new partially mode‐dependent filter is established via using a mode‐dependent Lyapunov function, where the stochastic property of mode available to a filter is considered. Sufficient conditions for the existence of H _∞ filter are obtained as strict linear matrix inequalities. Finally, numerical examples are used to show the effectiveness of the given theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

Stability and stabilization of discrete‐time singular Markov jump systems with time‐varying delay

The stochastic stability and stochastic stabilization of time‐varying delay discrete‐time singular Markov jump systems are discussed. For full and partial knowledge of transition probabilities cases, delay‐dependent linear matrix inequalities (LMIs) conditions for the systems to be regular, causal and stochastically stable are given. Sufficient conditions are proposed for the existence of state feedback controller in terms of LMIs. Finally, two numerical examples to illustrate the effectiveness of the method are given. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust H∞ control of Markovian jump systems with uncertain switching probabilities

This paper is concerned with the robust H_∞ control problem for a class of Markovian jump systems with uncertain switching probabilities, whose uncertainties are assumed to be elementwise bounded. First, new criterion of H_∞ performance for such uncertain systems is given. Then, new sufficient condition for H_∞ controller is established as strict linear matrix inequalities. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

H∞ filtering for a class of stochastic Markovian jump systems with impulsive effects

In this paper, we discuss the problem of H_∞ filtering for a class of stochastic Markovian jump systems with impulsive effects. The aim is to design a stochastically stable filter, using the locally sampled measurements, which guarantee both the stochastic stability and a prescribed level of H_∞ performance for the filtering error dynamics. A sufficient condition for the existence of such a filter is given in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is obtained. A numerical example is provided to show the effectiveness of the proposed results. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust discrete‐time H∞ filtering with uncertain initial state

We consider the problem of finite‐horizon discrete‐time H_∞ filtering with uncertain initial state condition and establish the relationship between the conventional γ‐performance bound and a recently proposed performance measure. A sub‐optimal but more efficient approach to computing the filter for the new performance measure is also derived. Copyright © 2008 John Wiley & Sons, Ltd.     

Delay‐dependent robust stabilization for uncertain singular systems with multiple time‐varying state delays

In this note, the problem of delay‐dependent robust stabilization for singular systems with multiple time‐varying state delays has been investigated, and the problem is solved via state feedback controller in terms of a linear matrix inequality technique. Numerical examples are given to show the validity of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Exponential H∞ filter design for stochastic time‐varying delay systems with Markovian jumping parameters

In this paper, the exponential H_∞ filter design problem is investigated for a general class of stochastic time‐varying delay system with Markovian jumping parameters. The stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time‐varying. Attention is focused on the design of mean‐square exponentially stable and Markovian jump filter such that the filtering error systems are mean‐square exponentially stable and the estimation error satisfies a given H_∞ performance. By introducing some slack matrix variables, delay‐dependent sufficient conditions for the solvability of the above problem are presented in terms of linear matrix inequalities (LMIs). In addition, the decay rate can be a given positive value without any other constraints. When the proposed LMIs are feasible, an explicit expression of the desired H_∞ filter can be given. A numerical example is provided to illustrate the effectiveness of the proposed design approach. Copyright © 2009 John Wiley & Sons, Ltd.